AP Calculus BC Formulas & Concepts

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Definition of a Limit

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Definition of Continuity at x = a

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Squeeze/Sandwich Theorem

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Intermediate Value Theorem

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If f is continuous on [a, b] and y is a number between f(a) and f(b), then there exists a c in (a, b) such that f(c) = y (aka f(x) takes on every y-value between f(a) and f(b))

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Extreme Value Theorem

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If f is continuous on [a, b], then there exists a c and d in [a, b] such that f(c) ≥ f(x) and f(d) ≤ f(x) for all x (aka f has an absolute max value f(c) and absolute min value f(d))

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Mean Value Theorem

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